Maths - Issues with Relative Angles

There are some issues with taking the relative angle between two angles, especially if we use this formula:
atan2(v2.y,v2.x) - atan2(v1.y,v1.x)
as discussed on this page.

It is useful to keep in mind that:

So, as an example, lets look at two vectors which are 90° (π/2) apart relative to each other. It should not matter what coordinate system we use as follows:

first and second quadrant If v1 is in the first quadrant and v2 is in the second we might get:
atan2(-1,1) - atan2(1,1)
= 3/4π - 1/4π
= π/2
quadrant 2 and 3 If v1 is in the second quadrant and v2 is in the third we might get:
atan2(-1,-1) - atan2(-1,1)
= -3/4π - 3/4π
= -π3/2
adding 2π gives:
= π/2
quadrant 3 and 4 If v1 is in the third quadrant and v2 is in the forth we might get:
atan2(1,-1) - atan2(-1,-1)
= -1/4π + 3/4π
= π/2
quadrant 4 and 1 If v1 is in the forth quadrant and v2 is in the first we might get:
atan2(1,1) - atan2(1,-1)
= 1/4π + 1/4π
= π/2

So the angle between the vectors is always π/2.


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see also:

Correspondence about this page
  • This page arose from a forum discussion with Jason about calculating relative angles here.

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